# Prove the Following Trigonometric Identities Cos^2 a + 1/(1 + Cos^2 A) = 1 - Mathematics

Prove the following trigonometric identities

cos^2 A + 1/(1 + cos^2 A) = 1

#### Solution

We know that

sin^2 A + cos^2 A = 1

cosec^2 A - cot^2 A = 1

So,

cos^2 A + 1/(1 + cot^2 A) = cos^2 A + 1/(cosec A)

= cos^2 A + (1/cosecA)^2

= cos^2 A + (sin A)^2

= cos^2 A + sin^2 A

= 1

Concept: Trigonometric Identities
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 9 | Page 43